Dynamic Covariance Models for Multivariate Financial Time Series

The accurate prediction of time-changing covariances is an important problem in the modeling of multivariate financial data. However, some of the most popular models suffer from a) overfitting problems and multiple local optima, b) failure to capture shifts in market conditions and c) large computational costs. To address these problems we introduce a novel dynamic model for time-changing covariances. Over-fitting and local optima are avoided by following a Bayesian approach instead of computing point estimates. Changes in market conditions are captured by assuming a diffusion process in parameter values, and finally computationally efficient and scalable inference is performed using particle filters. Experiments with financial data show excellent performance of the proposed method with respect to current standard models

Kernel Belief Propagation

We propose a nonparametric generalization of belief propagation, Kernel Belief Propagation (KBP), for pairwise Markov random fields. Messages are represented as functions in a reproducing kernel Hilbert space (RKHS), and message updates are simple linear operations in the RKHS. KBP makes none of the assumptions commonly required in classical BP algorithms: the variables need not arise from a finite domain or a Gaussian distribution, nor must their relations take any particular parametric form. Rather, the relations between variables are represented implicitly, and are learned nonparametrically from training data. KBP has the advantage that it may be used on any domain where kernels are defined (Rd, strings, groups), even where explicit parametric models are not known, or closed form expressions for the BP updates do not exist. The computational cost of message updates in KBP is polynomial in the training data size. We also propose a constant time approximate message update procedure by representing messages using a small number of basis functions. In experiments, we apply KBP to image denoising, depth prediction from still images, and protein configuration prediction: KBP is faster than competing classical and nonparametric approaches (by orders of magnitude, in some cases), while providing significantly more accurate results

mgm: Estimating Time-Varying Mixed Graphical Models in High-Dimensional Data

We present the R-package mgm for the estimation of k-order Mixed Graphical Models (MGMs) and mixed Vector Autoregressive (mVAR) models in high-dimensional data. These are a useful extensions of graphical models for only one variable type, since data sets consisting of mixed types of variables (continuous, count, categorical) are ubiquitous. In addition, we allow to relax the stationarity assumption of both models by introducing time-varying versions MGMs and mVAR models based on a kernel weighting approach. Time-varying models offer a rich description of temporally evolving systems and allow to identify external influences on the model structure such as the impact of interventions. We provide the background of all implemented methods and provide fully reproducible examples that illustrate how to use the package

Machine learning model selection with multi-objective Bayesian optimization and reinforcement learning

A machine learning system, including when used in reinforcement learning, is usually fed with only limited data, while aimed at training a model with good predictive performance that can generalize to an underlying data distribution. Within certain hypothesis classes, model selection chooses a model based on selection criteria calculated from available data, which usually serve as estimators of generalization performance of the model. One major challenge for model selection that has drawn increasing attention is the discrepancy between the data distribution where training data is sampled from and the data distribution at deployment. The model can over-fit in the training distribution, and fail to extrapolate in unseen deployment distributions, which can greatly harm the reliability of a machine learning system. Such a distribution shift challenge can become even more pronounced in high-dimensional data types like gene expression data, functional data and image data, especially in a decentralized learning scenario. Another challenge for model selection is efficient search in the hypothesis space. Since training a machine learning model usually takes a fair amount of resources, searching for an appropriate model with favorable configurations is by inheritance an expensive process, thus calling for efficient optimization algorithms. To tackle the challenge of distribution shift, novel resampling methods for the evaluation of robustness of neural network was proposed, as well as a domain generalization method using multi-objective bayesian optimization in decentralized learning scenario and variational inference in a domain unsupervised manner. To tackle the expensive model search problem, combining bayesian optimization and reinforcement learning in an interleaved manner was proposed for efficient search in a hierarchical conditional configuration space. Additionally, the effectiveness of using multi-objective bayesian optimization for model search in a decentralized learning scenarios was proposed and verified. A model selection perspective to reinforcement learning was proposed with associated contributions in tackling the problem of exploration in high dimensional state action spaces and sparse reward. Connections between statistical inference and control was summarized. Additionally, contributions in open source software development in related machine learning sub-topics like feature selection and functional data analysis with advanced tuning method and abundant benchmarking were also made